Numerical implementation for reconstruction of inhomogeneous conductivities via Generalized Polarization Tensors

TL;DR

This paper presents numerical methods utilizing Generalized Polarization Tensors for reconstructing inhomogeneous conductivities, including stability analysis and practical demonstrations of the reconstruction process.

Contribution

It introduces a least squares approach based on Generalized Polarization Tensors for reconstructing conductivities and provides stability and resolution analysis.

Findings

Successful reconstruction of three different conductivity types

Stability analysis confirms robustness of the method

Numerical demonstrations validate the approach

Abstract

This paper deals with numerical methods for reconstruction of inhomogeneous conductivities. We use the concept of Generalized Polarization Tensors, which were introduced in [3], to do reconstruction. Basic resolution and stability analysis are presented. Least square norm methods with respect to Generalized Polarization Tensors are used for reconstruction of conductivities. Finally, reconstruction of three different types of conductivities in the plane is demonstrated.